Question

Factor completely 4x^2 − 32

Answer 1

Answer: $4(x+2\sqrt{2})(x-2\sqrt{2})$

Step-by-step explanation:

We can first take out the common factor of 4, as both 4x² and -32 are divisible by 4.

$4(x^2-8)$

From here, we can assume that x²-8 is a difference of two squares even though 8 is not a perfect square.

For review, a difference of two squares $a^2-b^2$ can be factored into $(a+b)(a-b)$.

$4(x^2-8)\\4(x+\sqrt{8})(x-\sqrt{8})\\4(x+2\sqrt{2})(x-2\sqrt{2})$